I'll scrounge around for some hotels that are under $100. They are not easy to find. Even the Holiday Inn is going to run close to $200.
As for the Shedd's Aquarium, or any museum, get there EARLY the lines are insane, especially on the weekends.
Summer is beautiful here so you should have great weather. The park systems are terrific and free. Millenium Park is cool to visit, even though most locals don't like it, I do. Lincoln Park is great and the zoo is free if you are into that type of stuff.
Suggestion #1. By a day pass for the CTA or even a 5 day pass. It's $2 to get somewhere one-way and to have eto fill up on the machines is a pain. So if you are planning on using the El and busses a lot, I'd suggest it.
Also, if we are in town when you are in, we can get the Chicago crowd together and have a mini meet-up for dinner if you'd like.
I'll be back with more, but now I'm off to work.